MIT Cheetah 로봇의 탄생

석상옥 Naver Labs

contents

1. Introduction 2. Leg Actuation System Design 3. Parallel Processing in Mobile Robot Controllers 4. Design Principles for Energy Efficient Legged Locomotion 5. What’s Next?

1. Introduction

1. Introduction

http://www.youtube.com/watch?v=KYKg9-T2eNU 2012 BMW 3 Series Production - BMW Munich Plant - Body Shop

BMW 3 Series Production Boston Dynamics Atlas

Manufacturing Robot vs. Mobile Robot

1.1 Running

[1] P. WEYAND et al., “Faster top running speeds are achieved with greater ground forces not more rapid leg movements”, J. Appl. Physiol. 89: 1991–1999, 2000

𝐹 𝑧 (

N) 𝑇

𝑡𝑠 𝑡𝑠 𝑡𝑎 𝑡𝑎

M=70 kg V=4.5 m/s

700N

𝐹𝑧(𝑡) ⅆ𝑡 = 𝑚𝑔𝑇

𝑇

0

Vertical Momentum Conservation

1.2 In the Blink of an Eye

Airbag: 30ms

Playback speed: 0.06x MIT Cheetah running at 6m/s • Swing time: 250ms • Stance time: 57ms

Blink: 400ms

1.3 Requirements • Ground reaction force at 6m/s:

– Maximum: 450N

– Stance time: 57ms

• Leg actuation system’s force bandwidth:

– 120Hz (MIT Cheetah’s real spec)

• Main controller’s control sampling frequency:

– 20~30x of the closed loop bandwidth [64]

– 2.4-3.6kHz

– At 4 kHz, sampling period is 250𝜇𝑠

Fy

57ms

Touchdown angle

2. Leg Actuation System Design

Seok, Sangok, et al. "Actuator design for high force proprioceptive control in fast legged locomotion." Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on. IEEE, 2012.

2.1EM Motors

Recommended operation range

Short-term operation range

Torque

Angular speed

Maximum Continuous

Torque/Current

Demagnetization Torque/Current

10X of max. cont. Torque/Current

V= Vrecommended

𝑟 𝑡

𝑙

𝑟 : gap radius 𝑡 : rotor thickness 𝑙 : rotor length

Stator

Rotor

Torque Density ∝ 𝑟

2.2 Force Control

Geared Motor with Torque(Force) Sensor

Leg

Motor

High Gear Ratio Transmission

Stiff Sensor

Series Elastic Actuator

Leg

Spring, Encoder

Motor

High Gear Ratio Transmission

2.3 High Force Proprioceptive Actuation

High Torque Density Motor

Low Gear Ratio Transmission

Low Inertia Leg

No Force (Torque) Sensor No Series Elastic

Proprioceptive Actuation: Collocated force control through (1) maximizing torque density (2) minimizing mechanical impedance

2.4 Impedance Control

0

50

100

150

200

250

Time(ms)

400 0 50 100 150 200 250 300 350

Fo

rce(N

)

k=5,000N/m, d=100Ns/m Commanded Force Sensor

5cm

Force

Sensor

Sorbothane

Foot

3. Parallel Processing in Mobile Robot Controllers

A Highly Parallelized Control System Platform Architecture using Multicore CPU and FPGA for Multi-DoF Robots Sangok Seok, Dong Jin Hyun, SangIn Park, David Otten, and Sangbae Kim Submitted: 2014 IEEE International Conference on Robotics and Automation (ICRA)

3.1 Importance of Fast Processing MIT Cheetah: 12 DoF

Asimo: 34 DoF

More Functions (More Actuators and Sensors) More Agile (Higher System Bandwidth)

3.2 Solutions Faster system: - Faster Bus - Faster CPU [66],[67]

Main Controller Fast CPU

Distributed Controller 1

⋮ Distributed Controller 2

Distributed Controller N

Main Controller Multicore CPU, FPGA

Distributed Controller 1

⋮ Distributed Controller 2

Distributed Controller N

Fast BUS Parallel connection

Parallel Processing: - Parallel connection - Multicore CPU, FPGA

3.3 Parallel Processing

Single Worker:

1. Task Parallelism

Wash Iron Dry

4h 5h 6h

Dish Vacuum Cook

1h 2h 3h

Wash Iron Dry

1h 2h 3h

Worker 1:

Worker 2:

Worker 3:

Vacuum

Cook

Dish

4h 1h 2h 3h

Vacuum

Cook

Dish

4h

Wash

Iron

Dry

Vacuum

Cook

Dish

Wash

Iron

Dry

Wash

Dry

Iron

Vacuum

Cook

Dish

5h 6h

= 6 Tasks, 6 Hour

= 6 Tasks, 4 Hour = 6 Tasks, 1 Hour

Worker 1:

Worker 2:

Worker 3:

Worker 4:

Worker 5:

Worker 6:

2. Pipelining

Independent Dependent

3.4 Processing Sequence in MIT Cheetah

Forward Kinematics

Running Algorithm

PD Control Jacobian Current

Commands Receive

Sensor Data

Distributed Controller 1

Distributed Controller 2

Distributed Controller N

Main Controller ⋮

Ind

epen

den

t P

roce

ss

Dependent Process

3.5 Overall Process

Current 1 Current 2

: Current n

Current

Current

Current

Communication Output Emulator

Motor Driver 1

Motor Driver 2

.

.

.

Motor Driver n

.

.

.

Angle Current

Angle Current

Angle Current

Communication Input Emulator

Angle 1 Angle 2

: Angle n

Current 1 Current 2

: Current n

Front Left Leg Front Right Leg Rear Left Leg Rear Right Leg

Kinematics

.

.

.

𝑇1 = 17.24𝜇𝑠 𝑇2 = 22𝜇𝑠 𝑇3 = 50𝜇𝑠 𝑇4 = 44𝜇𝑠 𝑇5 = 36.85𝜇𝑠

3.6 Overall Process

𝜏1

𝜏2

𝜏3

𝜏4

𝜏5

𝜏1

𝜏2

𝜏3

𝜏4

𝜏5

𝜏1

𝜏2

𝜏3

𝜏4

𝜏5

𝜏1

𝜏2

𝜏3

𝜏4

𝜏5

Worker 1:

Worker 2:

Worker 3:

Worker 4:

𝜏1

𝜏2

𝜏3

𝜏4

𝜏5 Worker 5:

System throughput is governed by the slowest worker: 50us (Worker 3)

3.7 Process in Dualcore

Forward Kinematics

Running Algorithm

PD Control Jacobian Current

Commands Receive

Sensor Data

Main Controller

Think (Process)

Act (Transmit)

Sense (Receive)

Main Controller

Dualcore CPU

3.7 Process in Dual-core

𝑇𝑘 𝑅𝑘 𝑃𝑘 𝑇𝑘+1 𝑅𝑘+1 𝑃𝑘+1

Time

· · · · · ·

∆𝑇𝑅 ∆𝑇𝑃 ∆𝑇𝑇

∆𝑇

CPU

𝑇𝑘 𝑅𝑘

𝑃𝑘

𝑇𝑘+1 𝑅𝑘+1

𝑃𝑘+1

Time

· · · · · · CPU 2

CPU 1

∆𝑇

𝑘𝑡ℎ iteration 𝑘 + 1𝑡ℎ iteration

Single CPU

Dual-core CPU

3.7 Process in Dual-core

idle

idle

𝑇𝑘 𝑅𝑘

𝑃𝑘

Time

· · · · · · CPU 2

CPU 1

∆𝑇

𝑘𝑡ℎ iteration

𝑇𝑘+1 𝑅𝑘+1

𝑃𝑘+1

𝑘 + 1𝑡ℎ iteration

idle

idle 𝑇𝑘+2 𝑅𝑘+2

𝑃𝑘+2

𝑇𝑘+3 𝑅𝑘+3

𝑃𝑘+3

𝑇𝑘−1 𝑅𝑘+3 𝑇𝑘 𝑅𝑘

𝑃𝑘

𝑇𝑘+2 𝑅𝑘+2

𝑃𝑘+2

Time

· · · · · · CPU 2

CPU 1

∆𝑇 2

𝑘𝑡ℎ iteration

𝑇𝑘+1 𝑅𝑘+1

𝑃𝑘+1

𝑘 + 1𝑡ℎ iteration

Make ∆𝑇𝑃𝑟𝑜𝑐𝑒𝑠𝑠 = ∆𝑇𝑅𝑒𝑐𝑒𝑖𝑣𝑒 + ∆𝑇𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑡

Removing the idle states

3.8 Final Magic: SIMD Scalar Operation a=[1 3 5 7]; b=[2 4 6 8]; for i=1:4 c(i)=a(i)+b(i); end

SIMD Operation a=[1 3 5 7]; b=[2 4 6 8]; c=a+b;

a0 b0 c0

a1 b1 c1

a2 b2 c2

a3 b3 c3

+ =

+ =

+ =

+ =

a0 b0 c0

a1 b1 c1

a2 b2 c2

a3 b3 c3

+ =

3.8 Final Magic: SIMD

Benchmark test results with many legs: 1. PD Control 50000

0

10000

20000

30000

40000

1000 0 200 400 600 800

Number of Legs

Exe

cuti

on

Tim

e (n

s)

20

0

5

10

15

1000 0 200 400 600 800

Number of Legs

Scalar Operation

SIMD Operation

2500 times faster for 1000 legs

4. Design Principles for Energy Efficient Legged Locomotion

Design Principles for Highly Efficient Quadrupeds and Implementation on the MIT Cheetah Sangok Seok, Albert Wang, Meng Yee (Michael) Chuah, David Otten, Jeffrey Lang and Sangbae Kim 2013 IEEE International Conference on Robotics and Automation (ICRA)

Design Principles for Energy Efficient Legged Locomotion and Implementation on the MIT Cheetah Sangok Seok, Albert Wang, Meng Yee (Michael) Chuah, Dong Jin Hyun, Jongwoo Lee, David Otten, Jeffrey Lang, and Sangbae Kim 2014 IEEE/ASME Transactions on Mechatronics

4.1 Energy Flow Diagram

Energy Source (Battery)

Actuator (EM Motor)

Positive work

(Wposi)

Mechanical Transmission

Ej

Negative work

(Wneg)

Mechanical Energy (Ek + Ep)

Ef

Ei

Principles Implementation System Energy Flow

High Torque Density Motor

Energy Regeneration

Low Impedance Transmission

(Back Drivability)

Low Inertia Leg

Large Gap Radius Motor

Efficient Driver Design

Single-stage Low Gear Transmission

Dual Coaxial Motor

Differential Actuated Spine

Composite Leg/ Biotensegrity

Joule Heating

Friction

Interaction

4.2 Energy Regeneration

Deceleration Acceleration

Touch Down Lift Off

m

Stance Phase Flight Phase

Ground

4.3 Energy Efficiency for Animals and Robots

MIT Cheetah (0.5)

ASIMO (2) Bigdog (15)

Human Running

Cheetah

Log

Min

imu

m c

ost

of T

ran

spo

rt, P

/(W

V)

Eff

icie

ncy

Hig

her

(lo

g s

cale

)

5. What’s Next?

5.1 MIT Cheetah 2, Hermes